Role of defective icosahedra in undercooled copper
Massimo Celino and Vittorio Rosato*
ENEA, Ente per le Nuove Tecnologie, Energia e Ambiente, Centro Ricerche Casaccia, Casella Postale 2400, 00100 Roma, Italy
Andrea Di Cicco
†
IMPMC, Université Paris 6 et 7, CNRS, IPGP, 140 rue de Lourmel, 75015 Paris, France
Angela Trapananti
European Synchrotron Radiation Facility, 6 Rue Jules Horowitz, Boîte Postale 220, F-38043 Grenoble Cedex, France
Carlo Massobrio
Institut de Physique et de Chimie des Matériaux de Strasbourg, 23 rue du Loess, Boîte Postale 43, F-67034 Strasbourg, Cedex 2, France
Received 23 February 2007; published 31 May 2007
We elucidate the role played by defective icosahedra on the stability of undercooled copper by using
molecular-dynamics simulations. Our approach is substantiated by the level of agreement with experiments on
a variety of structural properties. We show that not only perfect but also defective icosahedra, embedded in a
disordered matrix, lower the local cohesive energy. This has the effect of stabilizing the liquid structure against
crystallization. Our work rationalizes experimental findings by identifying the nature of those icosahedral
subunits that contribute to the stability of the undercooled liquid.
DOI: 10.1103/PhysRevB.75.174210 PACS numbers: 61.20.Ja, 61.25.Mv, 64.70.Dv
The remarkable stability of undercooled metals against
crystallization has fostered intense research efforts since the
pioneering studies of Turnbull.
1
The physical nature of this
phenomenon has proved to be largely elusive, calling for
interpretations based on atomic-scale arguments. In the
search of the microscopic origins underlying this stability,
the role played by the icosahedral short-range order ISRO
has been frequently invoked.
2,3
A conclusive assessment of
the ISRO has proved to be challenging for both experiments
and theory.
4–8
In this paper, we provide a quantitative de-
scription of ISRO in a prototypical undercooled metal cop-
per and a rationale for its stability against crystallization.
Our calculations settle the controversy on the number of
icosahedral structural units by substantially enriching the in-
dications of previous phenomenological analysis.
5,8
We use
extensive molecular-dynamics MD simulations, based on
an n-body interatomic potential derived by a second-moment
approximation of the tight-binding scheme for d-band tran-
sition metals.
9
The topology of the local structure is charac-
terized in terms of a common-neighbor analysis and total-
energy calculations. This allows us to identify a the nature
of ISRO in terms of defective icosahedral clusters, b the
role played by the ISRO to stabilize the undercooled liquid,
and c the driving force for this stabilization in terms of
atomic energy contributions.
MD simulations are widely used to characterize both the
glassy and the liquid phase of metals
10–14
in terms of ISRO.
The classical version of MD, based on empirical potentials,
has proved to be highly reliable in describing the structural
features of metals in very diverse thermodynamic conditions,
including undercooled metals.
9,10,15,16
A recent paper on liq-
uid nickel has demonstrated that effective-pair potentials can
lead to a close agreement with first-principles molecular-
dynamics simulations.
17
In the specific case of liquid copper,
no intrinsic loss of accuracy is encountered since the perfor-
mances of potentials and first-principles schemes have been
found comparable.
12
In the present work, we rely on classical
interatomic potentials to afford system sizes and temporal
trajectories not currently achievable within the first-
principles MD approach.
11,12,18
We are able to collect a sta-
tistically significant number of configurations involving at-
oms participating to ISRO.
Three systems of 4000 atoms, initially arranged in fcc
crystal structures in cubic cells of linear sizes L =38.47 Å,
L =38.14 Å, and L = 30.01 Å, were subsequently melted to
reproduce liquid and undercooled copper at zero pressure
and at the temperatures T =1623 K, T =1400 K, and T
= 1313 K. In each simulation, the average distance covered
by the atoms in the liquid more than 40 Å ensures that the
final configurations retain no memory of the initial geom-
etries. The quench from the equilibrated liquid states T
=2000 K down to the three temperatures has been per-
formed in the NPT ensemble using the Parrinello-Rahman
and Nosé
19
scheme. For the liquid at T =1623 K and T
=1400 K and the undercooled T =1313 K liquid copper
structures, the densities agree with the experimental values
20
within 5%. After 100 ps of annealing at the final tempera-
ture, statistical averages and relevant data for structural
analysis have been calculated over time trajectories of
200 ps. Hereafter, we shall concentrate on the results at T
=1623 K and T =1313 K.
Recent experimental studies have confirmed the presence
of ISRO in simply undercooled metals, with no consensus on
the fraction of atoms involved and on the nature of the sub-
structural icosahedral units.
4–8
By following an alternative
strategy, the reverse Monte Carlo RMC method, combined
with accurate x-ray-absorption spectroscopy XAS, led to an
estimate for the fraction of nearly icosahedral clusters.
5,8
These results substantiated the presence of defective icosa-
hedra units. Given these pieces of evidence, unambiguous
theoretical tools are expected to bring new, compelling infor-
mation.
PHYSICAL REVIEW B 75, 174210 2007
1098-0121/2007/7517/1742105 ©2007 The American Physical Society 174210-1